Plastic gears

The Plastic module rates cylindrical spur and helical gear pairs in which at least one gear is a thermoplastic. Plastics lose stiffness and strength quickly as they warm up, so the rating starts from the tooth temperatures of a heat balance, then checks the tooth root and the flank with the strength at those temperatures, and adds the wear depth and the tip deformation. It follows VDI 2736 Part 2.

Inputs

Choose + Steel on POM or + PA66 on POM, dry above the list. The inspector groups:

Gears

Pinion teeth z₁, Wheel teeth z₂, Normal module mₙ (mm), Face width b (mm), Pressure angle αₙ (20°), Helix angle β (0°), Profile shift x₁ and Profile shift x₂. The geometry is that of the gear pair module, generated by the basic rack.

Materials

Pinion and Wheel: POM, PA66, PA66 GF30, PEEK (each "typical values") or Steel (not rated). At least one gear must be plastic. A steel gear gets its root stress listed but is not rated here; rate it as a steel gear pair if it matters.

The typical table's temperature limits are 100 °C for POM, 120 °C for PA66, 130 °C for PA66 GF30 and 150 °C for PEEK. Between its temperature points the modulus and strengths are interpolated linearly in temperature, and between 10⁶ and 10⁸ cycles log-linearly.

Load

Pinion torque (N·m), Pinion speed (rpm), Application factor Kₐ and Life (h, 5000 by default).

Lubrication and heat

Lubrication: Dry, Greased (once, at assembly) or Oil.
Friction μ: empty takes 0.20 dry on steel, 0.30 dry plastic on plastic, 0.09 greased, 0.04 oiled.
Housing: Open, Partly open or Closed, with Housing surface (m²) for the last two. A closed housing keeps the heat in and raises the tooth temperatures.
Ambient temperature ϑ₀ (23 °C; the oil temperature for an oiled pair) and Relative duty ED (running time over the whole time, 0–1).

Own material data

Rows of ϑ, E, σF at 10⁶ and 10⁸ cycles and σH at 10⁶ and 10⁸ cycles, by rising temperature, for the pinion and the wheel. Any rows replace the table's data for that gear. From the command line a wear coefficient and the highest permissible temperature can be given as well (pinionData, wheelData).

Requirements

Min root safety (2), Min flank safety (lubricated) (1.4), Max wear (0.1 × mₙ) and Max tip deformation (0.07 × mₙ), the recommendations of VDI 2736-2.

Results

The view card draws the mesh in the transverse section and shows Temperatures and safeties for the rated plastic gear. The key figures are Flank temperature (with the root temperature and the material's limit), Root safety, Flank safety and Tip deformation (with the wear). Details lists the pair geometry, load, heat, the elasticity factor ZE and each gear's temperatures, stresses, strengths and wear.

In 3D the pair is built at its real sizes and centre distance, each gear in plastic or steel; hovering turns them in mesh. The 2D and 3D tabs above the drawing switch to a 3D model; the choice is kept for the module. In 3D, drag to orbit and scroll to zoom; the model stands still and plays its motion once when the pointer moves onto it or it gets the keyboard focus (never with reduced motion). Without WebGL the drawing stays, with a note.

The Plastic gears template holds two pairs:

Result	PL1 Motor stage	PL2 Appliance stage, dry
Pair	20/40, mₙ 1 mm, b 20 mm, steel pinion, POM wheel, greased	25/50, mₙ 0.8 mm, b 8 mm, PA66 pinion, POM wheel, dry
Load	0.4 N·m at 1000 rpm (41.89 W)	0.15 N·m at 300 rpm (4.712 W)
Flank temperature	wheel 27.76 °C	pinion 47.86 °C, wheel 35.43 °C
Root safety SF	wheel 6.302	pinion 4.866, wheel 6.353
Flank safety SH	wheel 1.54	not checked (dry)
Wear	wheel 0.009744 mm	pinion 0.03256 mm, wheel 0.005606 mm
Tip deformation	0.005629 mm against 0.07 mm	0.01413 mm against 0.056 mm

What the results mean

Temperatures: the flank and root temperatures of each plastic gear from the friction power P·μ·HV, the loss factor HV of the mesh, the heat transfer of the teeth and the housing, and the duty. The check holds the flank temperature against the material's limit.
Root safety: the root stress with the load at the tip (form factors of ISO 6336-3) against the root strength at the root temperature and the gear's load cycles.
Flank safety: the flank stress with ZE from the moduli at the flank temperatures against the flank strength. It applies to lubricated gears only; a dry pair gets the note "dry running: wear governs".
Wear: the wear depth over the life from the friction work along the involute flank and the wear coefficient (a fifth of it greased, none oiled). Without a wear coefficient in own data, wear is not rated.
Tip deformation: the elastic deflection of the tooth tip against 0.07·mₙ; a larger deformation disturbs the mesh as the deflected tip enters it early.

The first template pair run dry instead of greased: the friction rises from 0.09 to 0.20, the wheel's flank temperature from 27.76 to 33.58 °C, and the wear from 0.009744 mm to 0.04872 mm, about half of the 0.1 mm limit.

Fixing a failing check

Temperature: lubricate (grease or oil), lower the friction, open the housing or give it more surface, reduce the duty, or choose a material with a higher limit (PA66 GF30, PEEK).
Root safety: larger module or face width, a positive shift on the weaker gear, a stiffer or stronger material at the operating temperature, a lower tooth temperature.
Flank safety: wider face, larger centre distance, lubrication.
Wear: lubrication, a lower friction, a wider face, a more wear-resistant material.
Tip deformation: larger module, a stiffer material (glass-filled), a lower temperature.

Standards and scope

VDI 2736 Part 2 for the temperatures, root, flank, wear and deformation, with the geometry, contact ratios and ZH of the ISO 6336 gear pair and the form factors of ISO 6336-3. The loss factor HV follows the Ohlendorf relation.

Not covered: the material values of VDI 2736 itself (the table's are typical values), moisture uptake and its effect on PA, creep under long standstill loads, the steel gear's own rating, and mounting the pair on the project's shafts.

From the command line

axm new plastic.axm.json --template plastic-gears
axm plastic-gear update plastic.axm.json PL1 --patch '{"lubrication":"dry"}'
axm solve plastic.axm.json